Here we, as others in the past [1]}, [2]}, use the mapping between the threshold model and the random field Ising model so that it is possible also to apply tools from statistical physics to the question. Another possibly useful analogy can be made between the TM and a spin gas. We neglect the structure of the network and consider particles stochastically moving in uniform medium, and affected primarily by nearby particles. In this case, the mixing rate can be associated directly with thermodynamic temperature. There is then an analogy between the tendency of all spins to be at the lower equilibrium for small mixing rate in the original system, and low-temperature Bose-Einstein condensation in the spin gas [3]}. This mapping may be worth future study.
